ssembly nowadays is a hard thing to learn, not because it's difficult but
because people thinks that there is no reason to learn assembly! That's
not true... With assembly you can have total power above the computer, and
know exactly what he's doing. Try to remember that while trying to learn!
You may wondering: Why to read this tut? Good point... There are thousands
of papers for programming assembly in x86. That's true... But did they
teach you how to make apps for linux? Did they talked about linux
interrupts? I don't think so... There are many tutorials about programming
assembly for x86 in dos and windows, but very few on linux. I want to
change that. So this is the first issue of a collection of papers about
that. If you find that this paper has any error, please contact me and let
me know.
##### Index #####
1. Numbering systems
1.1. Decimal system
1.2. Binary system
1.2.1. Converting a binary number to a decimal number
1.2.2. Converting a decimal number to a binary number
1.3. Hexadecimal system
1.4. Conventions
2. Binaries in computers
2.1. Bit
2.2. Nibble
2.3. Byte
2.4. Word
2.5. Double word
###################### 1. Numbering systems ######################
1.1. Decimal system
Nowadays we use the decimal numbering system in almost everything that is
related to numbers. We use it so often and in a natural way that we forget
it's meaning. What is decimal system?
. Every decimal number, has only digits between zero and nine,
making a total of 10 digits
Note: how many fingers do you have? ...10. In fact the decimal
system is bound to human anatomy.
. Ok, and what is the meaning of each digit? Consider the
following numbers: 234 and 234,43
We do some transformations
-> 234 i.e. 200 + 30 + 4 i.e. 2 * 10^2 + 3 * 10^1 + 4 * 10^0
-> 234,43 = 2 * 10^2 + 3 * 10^1 + 4 * 10^0 + 0,43 = 2 * 10^2 + 3 *
10^1 + 4 * 10^0 + 4 * 10^-1 + 3 * 10^-2
Do you see the relation? Each digit appearing to the left of the
decimal point represents a value between zero and nine times an increasing
power of ten. Digits appearing to the right of the decimal point represent
a value between zero and nine times a decreasing power of ten.
1.2. Binary system
Binary system uses only two digits, by convention the digits are 0 and 1.
This system is so widely used in computers... By coincidence or not this
system adjusts perfectly to computers... Computers operate using binary
logic. The computer represents values using two different voltage levels,
in this way we can represent 0 and 1. Like I said before the same applies
to binary system, it is well adjust to computer anatomy!
1.2.1. Converting a binary number to a decimal number
Apply the same rule we saw in 1.1, but with powers of two.
Example: 1010 -> 1 * 2^3 + 0 * 2^2 + 1 * 2^1 + 0 * 2^0 = 10
1.2.2. Converting a decimal number to a binary number
We have two ways to do it:
1.2.2.1 We consecutively divide the decimal value by a power
two(keeping the remainder), while the result of the division is different
than zero. The binary representation is obtained by the sequence of
remainders in the inverse order of the divisions.
Consider the number 10(in decimal):
10 / 2
0 5 / 2
1 2 / 2
0 1 / 2
1 0
So in binary we write 1010
1.2.2.2 You can try to find out the number by adding powers of two,
that added will produce the decimal result.
Consider for example number 123... hmmm it's a number not less than 2^0
and not greater then 2^7. Cool…
2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0
0 1 1 1 1 0 1 1 because 1 * 2^6 + 1 * 2^5 + 1 *
2^4 + 1 * 2^3 + 0 * 2^2 + 1*2^1 + 1 * 2^0
= 123
Our result is 1111011.
1.3. Hexadecimal system
You saw how many digits took to represent the number 123 in binary. 7
digits! Imagine 1200, 10000,... it hurts. So programmers had to choose
another numbering system, just to "talk" to the machine... and no... it's
not the decimal system!! You saw the trouble we had to convert one simple
number like 10 between decimal and binary... I think you don't want to
spend half of your life doing that. Engineers thought on that and they
elected the hexadecimal system... Hexadecimals is the "english" for
computers. They have two special features:
- They're very compact
- it's simple to convert them to binary and vice-versa. A
hexadecimal number has digits with a value between 0 and 15 times a
certain power of sixteen. Because we only know digits between 0-9 we have
to use six more digits! We can use the 6 first letters of the alphabet.
Let's see a example: FF = 15 * 16^1 + 15 * 16^0 = 255 (16) (10)
Converting between binary and hexadecimal is very easy! To convert binary
to hexadecimal remember that every four digits correspond to a single
hexadecimal digit... to convert back to binary just apply the inverse
rule! Let's take a look at the next example:
110 1011 = 0110 1011 =6B
(2) (16)
It's very easy!! To make things easier, take a look at the following
table:
################
# D # H # B #
################
# 0 # 0 # 0000 #
# 1 # 1 # 0001 #
# 2 # 2 # 0010 #
# 3 # 3 # 0011 #
# 4 # 4 # 0100 #
# 5 # 5 # 0101 #
# 6 # 6 # 0110 #
# 7 # 7 # 0111 #
# 8 # 8 # 1000 #
# 9 # 9 # 1001 #
#10 # A # 1010 #
#11 # B # 1011 #
#12 # C # 1100 #
#13 # D # 1101 #
#14 # E # 1110 #
#15 # F # 1111 #
################
1.4. Conventions
Programming in assembly, requires you to obey some rules when using
numbers, because you can use three different numbering systems.
When writing a number:
- all numbers have to start with a decimal digit
- all numbers end with a letter, indicating the type of number:
. for hexadecimals the letter is h
. binary numbers end with b
. decimals end with t or d We will use the following notation:
Xn Xn-1 ... X2 X1 -> Xi represents a bit, and i<-[0,1,...,n] represents
it's position.
######################## 2. Binaries in computers ########################
2.1. Bit is the abbreviation to binary digit. We'll use this abbreviation
all the time. As you may have guessed that “bit” is the smallest unit of
data on a binary computer.
2.2. Nibble is a set of four bits. For example 1110, 1101, 1111 is a
nibble... every thing that has 4 bits is a nibble.
X3 X2 X1 X0 -> X1 X0 are the low order bits in the nibble, while
X2X3 are the high order bits.
2.3. Byte -> This is the most used data structure in computers. A byte is
a collection of eight bits:
X7 X6 X5 X4 X3 X2 X1 X0 When referring to a byte we say that it's
low order nibble is X0 X1 X2 X3, while the high order nibble is X4 X5 X6
X7. Note: bytes are used to represent characters using the ASCII
character set.
2.4. A word consists of 2 bytes, i.e. a group of 16 bits. In a byte you
have a low order byte and high order byte.
2.5. A double word consists of 2 words, i.e. 4 bytes i.e. 32 bits. In a
double word you have a L.O. word and a H.O. word.
In the next tutorial I will talk about:
- Arithmetic operations - Signed and unsigned numbers - System
Organization - Flags and registers - Logical operations on bits - Some
instructions like: mov, jmp, call, and...
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